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# 35513 Statistical Methods

Warning: The information on this page is indicative. The subject outline for a particular session, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

Subject handbook information prior to 2020 is available in the Archives.

UTS: Science: Mathematical and Physical Sciences
Credit points: 6 cp

There are course requisites for this subject. See access conditions.

### Description

The ability to systematically collect, organise, analyse and interpret data are key professional skills. Data are generated from a wide variety of activities such as experimental records, surveys or consumer activity. This subject presents the conceptual framework and statistical techniques relevant to the synthesis of these data sets and their application to complex real-world problems. Topics covered include common distributions and data summaries, statistical tests for means and variance, standard experimental techniques for testing regression, significance and quality control. Students participate in an extension seminar focusing on the creative integration of learned technical skills and their ability to articulate the relevance of the mathematics being studied to their career.

### Subject learning objectives (SLOs)

Upon successful completion of this subject students should be able to:

1. Identify and justify statistical concepts and tools to analyse a real-world research problem Use appropriate statistical techniques to conduct exploratory data analysis and present numerical and graphical summaries. Apply inferences from sample data to populations Explain and relate the assumptions underlying the use of particular statistical techniques and check whether they are appropriate for a given data sample Conduct statistical analysis and interpret associated computer output Communicate clearly the results of a statistical analysis Relate to, and reflect on the role of statistical techniques covered in the subject in complex real-life applications and/or the broader social context. Effectively communicate to others, including non-specialist audiences, the contribution made by the specialist mathematical techniques learnt in the subject to the solution of a complex problem arising in a professional workplace or a broader social context

### Course intended learning outcomes (CILOs)

This subject also contributes specifically to the development of following course intended learning outcomes:

• Disciplinary knowledge and its appropriate application (1.0)
• An Enquiry-oriented approach (2.0)
• Professional skills and their appropriate application (3.0)
• Communication skills (6.0)

### Contribution to the development of graduate attributes

The Faculty of Science has determined that its courses will aim to develop the following attributes in students at the completion of their course of study. Each subject will contribute to the development of these attributes in ways appropriate to the subject and the stage of progression, thus not all attributes are expected to be addressed in all subjects.

Graduate Attribute 1 - Disciplinary knowledge and its appropriate application.

The lectures/tutorials and laboratory classes and exercises communicate knowledge and skills, and demonstrate how to apply both the knowledge and the skills to a variety of problems.

Graduate Attribute 2 - An Inquiry-oriented approach.

The lectures discuss various ways to address a particular question, and students will develop skills in determining the correct approach themselves in the laboratory classes.

Graduate Attribute 3 - Professional skills and their appropriate application.

The ability to work effectively and responsibly in a group is emphasised in the groupwork components of the in-class assessments. The use of specialist statistical software to implement straight-forward analyses of problems is assessed in the weekly exercises.

Graduate Attribute 4 - Ability and motivation for continued intellectual development.

The ability to independently collect and critically evaluate information is assessed in the in-laboratory critiquing tasks, where students must find articles in the media that use statistical methods and assess the use of statistical methods in the article.

Graduate Attribute 6 - Communication skills.

Presentation of written and oral solutions to problems using appropriate professional language is emphasised in the in-class assessments.

### Teaching and learning strategies

This subject introduces the principles and techniques of statistical analysis required in more advanced mathematical discourse, and develops practical skills in statistical analysis. In this way, students are equipped for a variety of possible later subjects in statistics and its applications; students also acquire foundational skills needed by the professional mathematician for ongoing learning.

Students are expected to attend two 1.5-hour lectures and one 1-hour postgraduate seminar session per week. Computer laboratory sessions (2 hours) are also available and strongly recommended.

Lectures will explain statistical concepts and techniques through both theoretical description and worked examples. Students should prepare by reviewing lecture material and other supporting information (videos, podcasts etc) available in UTSOnline, prior to attending lectures so that they can confirm their understanding through question and answer. The course follows a progression from basic concepts to more sophisticated topics. Weekly online quizzes aligned to lecture content are intended to consolidate the learning points, and encourage good personal organisation skills and effective time management. These quizzes will provide students with formative feedback s the are able to check their progress.

Computer laboratory activities are designed to aid visualisation and provide practice applying the concepts and techniques discussed in lectures. These activities are generally conducted in small groups.

The weekly postgraduate extension seminars are designed to develop the cognitive skills required to identify mathematical and statistical techniques relevant to the solutions of complex problems, and integrate learned technical skills. The seminars are intended to develop critical analysis of complex ideas, and articulation for a variety of audiences, the relevance of the mathematics being studied. The seminars provide the opportunity for students to relate the statistical and mathematical concepts both to their individual careers, and to the solution of complex problems arising in the broader social context.

Students should expect to spend at least six hours per week of individual or group study (including weekly online assessment tasks) in addition to lecture, laboratories and seminars.

Specific activities that students will need to perform during the semester to complete the Assessment Tasks are:

• Complete weekly online quizzes (these are automatically marked with immediate online feedback)
• Attend regular contact sessions with the subject coordinator/convenor as agreed at the first seminar to monitor and discuss progress on the learning tasks
• Develop professional and mathematical/statistical competencies through class contributions and activities relevant to individual career aspirations
• Access, and potentially contribute to, a collection of web-based resources focused on industry engagement and communication of mathematics
• Attend occasional special-focus seminars as advised during the semester on the engagement of mathematical sciences in industry.

### Content (topics)

The subject will cover topics selected from : descriptive statistics, normal distributions, relations in categorical data, design of experiments and sampling, probability and random variables, sampling distributions of proportion and mean, estimation and confidence intervals, hypothesis tests, simple regression and one-way ANOVA.

In the seminars students will be required to identify an area of activity in a professional workplace or a broader social context in which mathematical techniques play a critical role in the solution of complex problems.

For the chosen area, students will be required to describe:

• The nature of of the specific complex business/social problem or task whose solution relies on advanceed mathematical techniques, and the significance of that problem or task in the broader social or commercial context.
• How the mathematical techniques employed in the solution of the problem are related to the mathematica/statistical content of the subject, in terms accessible to an audience non-expert in mathematics

### Assessment

Intent: This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge and its appropriate application 2. An inquiry-oriented approach 3. Professional skills and their appropriate application 6. Communication skills This assessment task addresses subject learning objective(s): 1 This assessment task contributes to the development of course intended learning outcome(s): 1.0 Presentation Group, group and individually assessed 20% Assessment Task 1A: Individual/Group critical review of 1-2 pages Assessment Task 1B: Individual presentation for 3 mins Assessment Task 1C: Individual presentation for 5 mins Clear, legible and concise presentation of information Logical sequence of the topic Stage presence, eye contact, and vocal range Presentation timing Presentation slides enhancing topic

Intent: This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge and its appropriate application 2. An inquiry-oriented approach 3. Professional skills and their appropriate application 6. Communication skills This assessment task addresses subject learning objective(s): 7 and 8 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 3.0 and 6.0 Reflection Individual 15% Clarity of communication Style, appearance, and tone Grammar, spelling, and punctuation CV includes all required sections such as contact information, educational background, experience, skills, and interests The correctness of answers of student contributions in the classroom

#### Assessment task 3: Online exercises

Intent: This assessment task contributes to the development of the following graduate attributes: 1 - Disciplinary knowledge and its appropriate application. This assessment task addresses subject learning objective(s): 1 This assessment task contributes to the development of course intended learning outcome(s): 1.0 Exercises Individual 15% Completion of 10 Weekly Quizzes by their respective due dates; correctness of answers.

Intent: This assessment task contributes to the development of the following graduate attributes: 1. Disciplinary knowledge and its appropriate application 2. An Enquiry-oriented approach 3. Professional skills and their appropriate application 6. Communication skills This assessment task addresses subject learning objective(s): 1, 2, 3, 4, 5, 6 and 7 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0, 3.0 and 6.0 Examination Individual 50% correctness of answers accuracy of analysis quality of interpretation of computer outputs clarity of communication

### Minimum requirements

In order to pass this subject, a student must:

i) achieve a final result of 50% or more

AND

ii) must achieve 40% or more of the combined marks available for assessment tasks 1 to 4,

AND

iii) achieve 40% or more on the final examination.

The final mark result is the sum of the marks gained in each piece of assessment.

Students who obtain a final result of 50 marks or more, but fail to meet either or both of items ii) and iii) will be given an X grade (fail).

### Recommended texts

Statistics: The Art and Science of Learning from Data, 4thEdition 2017
Alan Agresti, Christine Franklin, Bernhard Klingenberg

Pearson: ISBN 9781292164830

The book is linked to questions that make up the online quizzes assigned for this course, and uses a package called ArtofStat to provide basic statistic summaries, graphs and tests.

Buy the eBook online direct from PEarson.. Details are under UTSOnline. Alternatively consider purchase through other online and physical retailers

See Link in UTSOnline > Orientation.

### Other resources

The topics covered by this course are taught in most First Year Stats courses at other institutions and in other textxbooks. If you seek additional information or clarification of a particular topic, you should consider viewing youtube videos or checking the relevant section of other textbooks. UTS also offers UPASS and the Maths and Science Study Centre services which you may find helpful. See Help and Support in the left hand panel of the UTSOnline page for this subject.